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Inexact Dual-Primal Isogeometric Tearing and Interconnecting Methods

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Domain Decomposition Methods in Science and Engineering XXIV (DD 2017)

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 125))

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Abstract

In Isogeometric Analysis (IgA), non-trivial computational domains are often composed of volumetric patches where each of them is discretized by means of tensor-product B-splines or NURBS. In such a setting, the dual-primal IsogEometric Tearing and Interconnecting (IETI-DP) method, that is nothing but the generalization of the FETI-DP method to IgA, has proven to be a very efficient solver for huge systems of IgA equations. Using IETI-DP, basically any patch-local solver can be extended to the global problem. So far, only direct solvers have been considered as patch-local solvers. In the present paper, we compare them with the option of using robust multigrid as patch-local solver. This is of special interest for large-scale patch-local systems or/and for large spline degrees, because the convergence of standard smoothers deteriorates with large spline degrees and the robust multigrid smoother chosen is only available on tensor-product discretizations.

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Notes

  1. 1.

    G+Smo (Geometry plus Simulation modules) v0.8.1, http://gs.jku.at/gismo.

  2. 2.

    Our code is compiled with the gcc 4.8.3 compiler with optimization flag -O3. The results are obtain on the RADON1 cluster at Linz. We use a single core of a node, equipped with 2x Xeon E5-2630v3 “Haswell” CPU (8 Cores, 2.4 GHz, 20 MB Cache) and 128 GB RAM.

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Acknowledgements

This work was supported by the Austrian Science Fund (FWF) under the grant W1214, project DK4, and via the NFN project S117-03. This support is gratefully acknowledged.

Author information

Authors and Affiliations

  1. Johannes Kepler University (JKU), Linz, Austria

    Christoph Hofer & Ulrich Langer

  2. Austrian Academy of Sciences, RICAM, Linz, Austria

    Ulrich Langer & Stefan Takacs

Authors
  1. Christoph Hofer
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  2. Ulrich Langer
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  3. Stefan Takacs
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Corresponding authors

Correspondence to Christoph Hofer , Ulrich Langer or Stefan Takacs .

Editor information

Editors and Affiliations

  1. Department of Informatics, University of Bergen, Bergen, Norway

    Petter E. Bjørstad

  2. Department of Mathematics, Louisana State University, Baton Rouge, LA, USA

    Susanne C. Brenner

  3. Laboratoire Analyse, Géométrie et Applications, Université Paris 13, Villetaneuse, France

    Lawrence Halpern

  4. Department of Applied Mathematics, Kyung Hee University, Yongin, Korea (Republic of)

    Hyea Hyun Kim

  5. FB Mathematik und Informatik, Freie Universität Berlin, Berlin, Germany

    Ralf Kornhuber

  6. Western Norway University of Applied Sciences, Bergen, Norway

    Talal Rahman

  7. Courant Institute of Mathematical Sciences, New York University, New York, NY, USA

    Olof B. Widlund

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Hofer, C., Langer, U., Takacs, S. (2018). Inexact Dual-Primal Isogeometric Tearing and Interconnecting Methods. In: Bjørstad, P., et al. Domain Decomposition Methods in Science and Engineering XXIV . DD 2017. Lecture Notes in Computational Science and Engineering, vol 125. Springer, Cham. https://doi.org/10.1007/978-3-319-93873-8_37

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